RMO Practice question 4

Algebra Level 4

\[ \sqrt{(2\lambda-3\mu)^{2}+ (2-4\lambda+3\mu)^{2}+(2\lambda-3)^{2}+4031^{2}} \geq \eta\]

Find the maximum integer value of \( \eta \), such that for all real numbers \(\lambda,\mu\), the inequality above is fulfilled.

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